diff options
| -rw-r--r-- | marginal.tex | 22 |
1 files changed, 11 insertions, 11 deletions
diff --git a/marginal.tex b/marginal.tex index 508b674..de44583 100644 --- a/marginal.tex +++ b/marginal.tex @@ -368,13 +368,13 @@ pseudogap. \begin{figure} \hspace{1.3em} - \includegraphics{figs/spectrum_less.pdf} + \includegraphics{spectrum_less.pdf} \hspace{-2em} - \includegraphics{figs/spectrum_eq.pdf} + \includegraphics{spectrum_eq.pdf} \hspace{-2em} - \includegraphics{figs/spectrum_more.pdf} + \includegraphics{spectrum_more.pdf} \\ - \includegraphics{figs/large_deviation.pdf} + \includegraphics{large_deviation.pdf} \caption{ The large deviation function $G_0(\mu)$ defined in \eqref{eq:large.dev} as a function of the shift $\mu$ to the @@ -1250,17 +1250,17 @@ Lagrange multiplier is larger than 2, then we have a marginal minimum made up of subspace and a stable minimum on the other. \begin{figure} - \includegraphics{figs/msg_marg_legend.pdf} + \includegraphics{msg_marg_legend.pdf} \vspace{1em} - \includegraphics{figs/msg_marg_params.pdf} + \includegraphics{msg_marg_params.pdf} \hfill - \includegraphics{figs/msg_marg_spectra.pdf} + \includegraphics{msg_marg_spectra.pdf} \vspace{1em} - \includegraphics{figs/msg_marg_complexity.pdf} + \includegraphics{msg_marg_complexity.pdf} \caption{ Properties of marginal minima in the multispherical model. @@ -1560,7 +1560,7 @@ Hessian cannot be done independently from the complexity, and the method introduced in this paper becomes necessary. \begin{figure} - \includegraphics{figs/most_squares_complexity.pdf} + \includegraphics{most_squares_complexity.pdf} \caption{ Dominant and marginal complexity in the nonlinear sum of squares problem for $\alpha=\frac32$ and $f(q)=q^2+q^3$. The ground state energy @@ -1579,7 +1579,7 @@ lowest energy significantly higher than the ground state and the highest energy significantly higher than the threshold. \begin{figure} - \includegraphics{figs/most_squares_stability.pdf} + \includegraphics{most_squares_stability.pdf} \caption{ The stability, or shift of the trace, for dominant and marginal optima in the nonlinear sum of squares problem for $\alpha=\frac32$ and @@ -1597,7 +1597,7 @@ which is the stability associated with the dominant complexity and coincides with the marginal stability only at the threshold energy. \begin{figure} - \includegraphics{figs/most_squares_complex.pdf} + \includegraphics{most_squares_complex.pdf} \caption{ Real and imaginary parts of the complexity $\Sigma_0(E,\mu)$ with fixed minimum eigenvalue $\lambda^*=0$ as a function of $\mu$ in the nonlinear |